1. Field of the Invention
The present invention relates to a system and method for determining a shape of a surface of an object and to a method of manufacturing an object having a surface of a predetermined shape. In particular, the invention relates to measuring and manufacturing objects having surfaces of an aspherical shape. The systems and methods may be applied to measuring and manufacturing objects such as an optical element.
2. Brief Description of Related Art
The optical element may comprise, for example, an optical component such as an optical lens or an optical mirror used in optical systems, such as telescopes used in astronomy, and systems used for imaging structures, such as structures formed on a mask or reticle, onto a radiation sensitive substrate, such as a resist, in a lithographic method. The success of such an optical system is substantially determined by the accuracy with which the optical surface can be machined or manufactured to have a target shape determined by a designer of the optical system. In such manufacture it is necessary to compare the shape of the machined optical surface with its target shape, and to determine differences between the machined and target surfaces. The optical surface may then be further machined at those portions where differences between the machined and target surfaces exceed e.g. predefined thresholds.
Interferometric apparatuses are commonly used for measurements of optical surfaces. Examples of such apparatus are disclosed in U.S. Pat. Nos. 4,732,483, 4,340,306, 5,473,434, 5,777,741, 5,488,477. The entire contents of these documents are incorporated herein by reference.
The conventional interferometer apparatus for measuring a spherical optical surface typically includes a source of coherent light and an interferometer optics for generating a beam of measuring light having spherical wavefronts. The measuring light is incident on the surface to be tested, such that wavefronts of the measuring light have, at a position of the surface to be tested, a same shape as the target shape of the surface under test. In such a situation, the beam of measuring light is orthogonally incident on the surface under test, and is reflected therefrom to travel back towards the interferometer optics. Thereafter, the light of the measuring beam reflected from the surface under test is superimposed with light reflected from a reference surface and deviations of the shape of the surface under test and its target shape are determined from a resulting interference pattern.
While spherical wavefronts for testing spherical optical surfaces may be generated with a relatively high precision by conventional interferometer optics, more advanced optics, which are also referred to as compensators, null lens arrangements, or K-systems, are used to generate beams of measuring light having aspherical wavefronts such that the light is substantially orthogonally incident at each location of the aspherical surface under test. Background information relating to null lens arrangements or compensators is available e.g. from the text book of Daniel Malacara “Optical Shop Testing”, 2nd Edition, John Wiley & Sons, Inc. 1992, Chapter 12.
For each application of measuring an aspherical surface of a particular type it is necessary to design and manufacture a corresponding null-lens arrangement for generating those aspherical wavefronts which are orthogonally incident on the aspherical surface of the particular type. This necessity limits flexibility in testing aspherical surfaces of various types.
From U.S. Pat. No. 5,004,346 there is known a method of testing aspherical surfaces using an interferometer optics generating spherical wavefronts. The spherical wavefronts are substantially orthogonally incident on the aspherical surface at only a portion thereof such that only this portion contributes to generation of interference fringes which are detected. By changing a distance between the interferometer optics and the aspherical surface to be tested it is possible to change the portions of the aspherical surface which contribute to generation of the detectable interference fringes. Thus, by testing the aspherical surface with the spherical wavefronts at plural distances of the aspherical surface from the interferometer optics, it is possible to test substantially the whole surface area of the aspherical surface and to calculate the surface shape thereof from the measurements taken at the plural distances.
For this purpose, it is necessary to precisely control the distance between the aspherical surface and the interferometer optics. Such method involves high requirements on actuators for translating the aspherical surface relative to the interferometer optics.